#19418: skew-Hadamard matrices and related srg's
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Reporter: | Owner:
dimpase | Status: needs_work
Type: | Milestone: sage-6.10
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers: Nathann Cohen
combinatorics | Work issues:
Keywords: | Commit:
Authors: | c5a7eee39d4c6dce006d1f6f8fd7a23383d540b7
Report Upstream: N/A | Stopgaps:
Branch: |
public/19418 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:14 ncohen]:
> First-pass review:
thanks, and apologies for sloppy code (back to Oxford with huge jetlag)
>
> - Why don't you call `normalise_hadamard` instead of adding a keyword
inside of
> `hadamard_matrix_paleyI` (without changing `hadamard_matrix_paleyII`)?
Those
> two functions are not directly available to the users, who are meant
to call
> `hadamard_matrix` directly.
`normalize_hadamard` does not do what I need; I need a different type of
normalization, in fact, where the matrix has the 1st row consisting of 1s,
and still H+H.T==2*I,
i.e. the 1st column of H is all -1 (with exception of the top left entry)
Should I perhaps introduce `skew_normalize_hadamard`,
that can only be applied to skew Hadamard matrices?
(I'd have uses for it in graph constructions, too)
>
> - `is_hadamard_martrix` -- could you move 'skew=False' to before
'verbose=False'
> ? Usually the verbosity/check flags are the last ones to appear as
they do not
> change the behaviour of the functon.
right. I forgot that keyword args can be positional, too...
>
> - Call `is_skew_symmetric` instead of doing it yourself. In theory you
shouldn't
> have to create two copies of the matrix in memory in order to check
that.
>
> - `zero_position=1` -- you have to write documentation for private
functions
> too. Does [the paraeter that you add] appear in the lemma cited in the
> docstring?
>
> - `zero_position=1` -- if you meant `True`, write `True`.
>
> - `_circulant_matrix` -- if it does not exist yet, this constructor
should be
> added in the matrix/ code and be available through `matrix.<tab>`
OK
>
> - `mod(j-i,n)` is `(j-i)%n`. One day you will have to accept that you
write
> Python code.
>
> - Instead of a `_GS_skew_hadamard` function that encodes 4 matrices, why
don't
> you reserve cases `if n == 36' (and others) in the main function
> `skew_hadamard_matrix`? That would also solve the problem that this
function
> has no documentation whatsoever.
I'd rather add documentation, thanks for reminding.
I find `skew_hadamard_matrix` already hard to read, and
it would positively turn ugly if I start adding that explicit data for
matrices there.
>
> - 'and' (see wikipedia:
https://en.wikipedia.org/wiki/Bitwise_operation#AND) is
> a useful operator in computer science. E.g.:
>
> {{{
> + if M is None: # try Williamson-Goethals-Seidel construction
> + if _GS_skew_hadamard(n, existence=True):
> }}}
> becomes
> {{{
> + if M is None and_GS_skew_hadamard(n, existence=True):
> }}}
oops - there is an extra `if` there that should go...
>
> - `switch_skewhad_pow2` -- please respect the current standard for the
names in
> `graphs.<tab>`. Upper case, no underscore, ends with `Graph`.
Actually, it
> could be named 'SwitchSkewhadGraph` and only mention the `pow2` part
in the
> docstring.
>
> - `graphs.Pseudo_L_2n_4n_m_1`? Seriously? If you cannot give it a clear
and
> meaningful name easily, then take it as a sign that this function
should not
> be exposed to the users directly.
How about we have a `PseudoLatinSquaresGraph(m,n)` or
`PseudoOrthogonalArrayBlockGraph(m,n)` ? (I'd prefer the former name; or
maybe we can have both?)
It would include `Pseudo_L_2n_4n_m_1` and `OrthogonalArrayBlockGraph` as
subcases.
(Perhaps there are more subcases, in fact, but we don't have to worry
about it now).
>
> - `_L_g_n_params` -- yes, please remove this function if you do not use
it.
sure.
--
Ticket URL: <http://trac.sagemath.org/ticket/19418#comment:15>
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